Basic Math Examples

$4 s + \frac{1}{3} - 6 s = - \frac{3}{4}$

Step 1

Subtract $6 s$ from $4 s$ .

$- 2 s + \frac{1}{3} = - \frac{3}{4}$

Step 2

Move all terms not containing $s$ to the right side of the equation.

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Step 2.1

Subtract $\frac{1}{3}$ from both sides of the equation.

$- 2 s = - \frac{3}{4} - \frac{1}{3}$

Step 2.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 2 s = - \frac{3}{4} \cdot \frac{3}{3} - \frac{1}{3}$

Step 2.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 2 s = - \frac{3}{4} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{4}{4}$

Step 2.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$- 2 s = - \frac{3 \cdot 3}{4 \cdot 3} - \frac{1}{3} \cdot \frac{4}{4}$

Step 2.4.2

Multiply $4$ by $3$ .

$- 2 s = - \frac{3 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}$

Step 2.4.3

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$- 2 s = - \frac{3 \cdot 3}{12} - \frac{4}{3 \cdot 4}$

Step 2.4.4

Multiply $3$ by $4$ .

$- 2 s = - \frac{3 \cdot 3}{12} - \frac{4}{12}$

Step 2.5

Combine the numerators over the common denominator.

$- 2 s = \frac{- 3 \cdot 3 - 4}{12}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 3$ by $3$ .

$- 2 s = \frac{- 9 - 4}{12}$

Step 2.6.2

Subtract $4$ from $- 9$ .

$- 2 s = \frac{- 13}{12}$

Step 2.7

Move the negative in front of the fraction.

$- 2 s = - \frac{13}{12}$

Step 3

Divide each term in $- 2 s = - \frac{13}{12}$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 s = - \frac{13}{12}$ by $- 2$ .

$\frac{- 2 s}{- 2} = \frac{- \frac{13}{12}}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 s}{- 2} = \frac{- \frac{13}{12}}{- 2}$

Step 3.2.1.2

Divide $s$ by $1$ .

$s = \frac{- \frac{13}{12}}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$s = - \frac{13}{12} \cdot \frac{1}{- 2}$

Step 3.3.2

Move the negative in front of the fraction.

$s = - \frac{13}{12} (- \frac{1}{2})$

Step 3.3.3

Multiply $- \frac{13}{12} (- \frac{1}{2})$ .

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Step 3.3.3.1

Multiply $- 1$ by $- 1$ .

$s = 1 (\frac{13}{12}) \frac{1}{2}$

Step 3.3.3.2

Multiply $\frac{13}{12}$ by $1$ .

$s = \frac{13}{12} \cdot \frac{1}{2}$

Step 3.3.3.3

Multiply $\frac{13}{12}$ by $\frac{1}{2}$ .

$s = \frac{13}{12 \cdot 2}$

Step 3.3.3.4

Multiply $12$ by $2$ .

$s = \frac{13}{24}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \frac{13}{24}$

Decimal Form:

$s = 0.541\overline{6}$